Name_________________________________
Period_____
PreCalculus
Homework 2.2 (day 2) Polynomial Functions
For each function, (a) determine the zeros and state the multiplicity of any repeated zeros,
(b) find the y-intercepts, and then
(c) graph the function.
1. f ( x)  ( x  2)2 ( x  4)2
2. g ( x)  2 x3  4 x 2  6 x
3. f ( x)  x5  3x 4  10 x3
Find a polynomial function of degree n with only the following real zeros. More than one answer is possible.
4. zeros: 0, 3, -2; n = 5
5. no real zeros; n = 6
For each of the following graphs:
(a) Determine the least possible degree and end behavior
(b) Locate the zeros and their multiplicity. Assume all of the zeros are integral values.
(c) Create a function that fits the graph and given point.
6.
7.
Create a function with the following characteristics. Graph the function.
8. Degree = 6, 4 real zeros, lim  
x
9. Degree = 6, 3 distinct real zeros, 1 of which has
a multiplicity of 2, lim  
x
Define the function with least degree with the following graph or conditions.
10.
11. zeros at -3(multiplicity 2) and 5(multiplicity 1)
6 turning points
y-intercept = (0,0)
lim f ( x)  
x 
f(x) is odd
11. Can a polynomial function have both an absolute maximum and an absolute minimum? Explain.
12. What is the least degree polynomial function that has an absolute maximum, a relative maximum, and a
relative minimum? Explain your reasoning.